ABSTRACTS
OF 
PART I: A GENERAL OVERVIEW 
In this chapter a critical comparison of Mtheory and TGD as two competing theories is carried out. Dualities and black hole physics are regarded as basic victories of Mtheory. a) The counterpart of electric magnetic duality plays an important role also in TGD and it has become clear that it might change the sign of Kähler coupling strength rather than leaving it invariant. The different signs would be related to different time orientations of the spacetime sheets. This option is favored also by TGD inspired cosmology. b) The AdS/CFT duality of Maldacena involved with the quantum gravitational holography has a direct counterpart in TGD with 3dimensional causal determinants serving as holograms so that the construction of absolute minima of Kähler action reduces to a local problem. c) The attempts to develop further the nebulous idea about spacetime surfaces as quaternionic submanifolds of an octonionic imbedding space led to the realization of duality which could be called number theoretical spontaneous compactification. Spacetime can be regarded equivalently as a hyperquaternionic 4surface in M^{8} with hyperoctonionic structure or as a 4surface in M^{4}× CP_{2}. d) The duality of string models relating KaluzaKlein quantum numbers with YM quantum numbers could generalize to a duality between 7dimensional light like causal determinants of the imbedding space (analogs of "big bang") and 3dimensional light like causal determinants of spacetime surface (analogs of black hole horizons). e) The notion of cotangent bundle of configuration space of 3surfaces suggests the interpretation of the numbertheoretical compactification as a waveparticle duality in infinitedimensional context. Also the duality of hyperquaternionic and cohyperquaternionic 4surfaces could be understood analogously. These ideas generalize at the formal level also to the Mtheory assuming that stringy configuration space is introduced. The existence of Kähler metric very probably does not allow dynamical target space. In TGD framework black holes are possible but putting black holes and particles in the same basket seems to be mixing of apples with oranges. The role of black hole horizons is taken in TGD by 3D light like causal determinants, which are much more general objects. Black holeelementary particle correspondence and padic length scale hypothesis have already earlier led to a formula for the entropy associated with elementary particle horizon. The recent findings from RHIC have led to the realization that TGD predicts black hole like objects in all length scales. They are identifiable as highly tangled magnetic flux tubes in Hagedorn temperature and containing conformally confined matter with a large Planck constant and behaving like dark matter in a macroscopic quantum phase. The fact that string like structures in macroscopic quantum states are ideal for topological quantum computation modifies dramatically the traditional view about black holes as information destroyers. The discussion of the basic weaknesses of Mtheory is motivated by the fact that the few predictions of the theory are wrong which has led to the introduction of anthropic principle to save the theory. The mouse as a tailor history of Mtheory, the lack of a precise problem to which Mtheory would be a solution, the hard nosed reductionism, and the censorship in Los Alamos archives preventing the interaction with competing theories could be seen as the basic reasons for the recent blind alley in Mtheory. 
PART II:PHYSICS AS INFINITEDIMENSIONAL SPINOR GEOMETRY IN THE WORLD OF CLASSICAL WORLDS 
In this chapter the classical field equations associated with the Kähler action are studied. The study of the extremals of the Kähler action has turned out to be extremely useful for the development of TGD. Towards the end of year 2003 quite dramatic progress occurred in the understanding of field equations and it seems that field equations might be in welldefined sense exactly solvable. Years later the understanding of quantum TGD at fundamental level deepened the understanding. 1. Preferred extremals and quantum criticality The identification of preferred extremals of Kähler action defining counterparts of Bohr orbits has been one of the basic challenges of quantum TGD. By quantum classical correspondence the nondeterministic spacetime dynamics should mimic the dissipative dynamics of the quantum jump sequence. It should also represent spacetime correlate for quantum criticality. The solution of the problem through the understanding of the implications number theoretical compactification and the realization of quantum TGD at fundamental level in terms of second quantization of induced spinor fields assigned to the modified Dirac action defined by Kähler action. Noether currents assignable to the modified Dirac equation are conserved only if the first variation of the modified Dirac operator D_{K} defined by Kähler action vanishes. This is equivalent with the vanishing of the second variation of Kähler action at least for the variations corresponding to dynamical symmetries having interpretation as dynamical degrees of freedom which are below measurement resolution and therefore effectively gauge symmetries. The vanishing of the second variation in interior of X^{4}(X^{3}_{l}) is what corresponds exactly to quantum criticality so that the basic vision about quantum dynamics of quantum TGD would lead directly to a precise identification of the preferred extremals. Something which I should have noticed for more than decade ago! The question whether these extremals correspond to absolute minima remains however open. The vanishing of second variations of preferred extremals suggests a generalization of catastrophe theory of Thom, where the rank of the matrix defined by the second derivatives of potential function defines a hierarchy of criticalities with the tip of bifurcation set of the catastrophe representing the complete vanishing of this matrix. In the recent case this theory would be generalized to infinitedimensional context. The spacetime representation for dissipation comes from the interpretation of regions of spacetime surface with Euclidian signature of induced metric as generalized Feynman diagrams (or equivalently the lightlike 3surfaces defining boundaries between Euclidian and Minkowskian regions). Dissipation would be represented in terms of Feynman graphs representing irreversible dynamics and expressed in the structure of zero energy state in which positive energy part corresponds to the initial state and negative energy part to the final state. Outside Euclidian regions classical dissipation should be absent and this indeed the case for the known extremals. 2. HamiltonJacobi structure Most known extremals share very general properties. One of them is HamiltonJacobi structure meaning the possibility to assign to the extremal so called HamiltonJacobi coordinates. This means dual slicings of M^{4} by string world sheets and partonic 2surfaces. Number theoretic compactification led years later to the same condition. This slicing allows a dimensional reduction of quantum TGD to Minkowksian and Euclidian variants of string model and allows to understand how Equivalence Principle is realized at spacetime level. Also holography in the sense that the dynamics of 3dimensional spacetime surfaces reduces to that for 2D partonic surfaces in a given measurement resolution follows. The construction of quantum TGD relies in essential manner to this property. CP_{2} type vacuum extremals do not possess HamiltonJaboci structure but this can be understood in the picture provided by number theoretical compactification. 3. Physical interpretation of extremals The vanishing of Lorentz 4force for the induced Kähler field means that the vacuum 4currents are in a mechanical equilibrium and dissipation is absent except in the sense that the superposition of generalized Feynman graphs representing the zero energy state represents dissipation. Lorentz 4force vanishes for all known solutions of field equations.
4. The dimension of CP_{2} projection as classifier for the fundamental phases of matter The dimension D_{CP2} of CP_{2} projection of the spacetime sheet encountered already in padic mass calculations classifies the fundamental phases of matter.
5. Specific extremals of Kähler action The study of extremals of Kähler action represents more than decade old layer in the development of TGD.

PART III: ALGEBRAIC PHYSICS 
PART IV: HYPERFINITE FACTORS OF TYPE II_{1} AND HIERARCHY OF PLANCK CONSTANTS 
PART V: APPLICATIONS 